@article{VMJ_2016_18_1_a5,
author = {A. G. Kusraev},
title = {Operators on injective {Banach} lattices},
journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
pages = {42--50},
year = {2016},
volume = {18},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/VMJ_2016_18_1_a5/}
}
A. G. Kusraev. Operators on injective Banach lattices. Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 1, pp. 42-50. http://geodesic.mathdoc.fr/item/VMJ_2016_18_1_a5/
[1] Kusraev A. G., “Boolean valued transfer principle for injective Banach lattices”, Siberian Math. J., 56:5 (2015), 888–900 | DOI | Zbl
[2] Abramovich Yu. A., “Weakly compact sets in topological Dedekind complete vector lattices”, Teor. Funkciĭ, Funkcional. Anal. i Priložen., 15 (1972), 27–35
[3] Lotz H. P., “Extensions and liftings of positive linear mappings on Banach lattices”, Trans. Amer. Math. Soc., 211 (1975), 85–100 | DOI | MR | Zbl
[4] Meyer-Nieberg P., Banach Lattices, Springer, Berlin etc., 1991, xvi+395 pp. | MR | Zbl
[5] Haydon R., “Injective Banach lattices”, Math. Z., 156 (1974), 19–47 | DOI | MR
[6] Aliprantis C. D., Burkinshaw O., Positive Operators, Acad. Press, N.Y., 1985, xvi+367 pp. | MR | Zbl
[7] Kusraev A. G., Dominated Operators, Kluwer, Dordrecht, 2000, 405 pp. | MR | Zbl
[8] Kusraev A. G., Kutateladze S. S., Boolean Valued Analysis, Selected Topics, SMI VSC RAS, Vladikavkaz, 2014, iv+400 pp.
[9] Bell J. L., Boolean-Valued Models and Independence Proofs in Set Theory, Clarendon Press, N.Y. etc., 1985, xx+165 pp. | MR | Zbl
[10] Kusraev A. G., Kutateladze S. S., Boolean valued analysis, Kluwer, Dordrecht a. o., 1995
[11] Takeuti G., Zaring W. M., Axiomatic set Theory, Springer-Verlag, N.Y., 1973, 238 pp. | MR | Zbl
[12] Gutman A. E., “Banach bundles in the theory of lattice-normed spaces”, Linear Operators Compatible with Order, Sobolev Institute Press, Novosibirsk, 1995, 63–211 (in Russian) | MR | Zbl
[13] Gutman A. E., “Disjointness preserving operators”, Vector Lattices and Integral Operators, ed. S. S. Kutateladze, Kluwer Acad. Publ., Dordrecht etc., 1996, 361–454 | MR
[14] Abramovich Y. A., Aliprantis C. D., An Invitation to Operator Theory, Amer. Math. Soc., Providence, R.I., 2002, iv+530 pp. | MR | Zbl
[15] Abramovich Y. A., “A generalization of a theorem of J. Holub”, Proc. Amer. Math. Soc., 108 (1990), 937–939 | DOI | MR | Zbl
[16] Schmidt K. D., “Daugavet's equation and orthomorphisms”, Proc. Amer. Math. Soc., 108 (1990), 905–911 | MR | Zbl
[17] Lindenstrauss J., Tzafriri L., Classical Banach Spaces, v. 2, Function Spaces, Springer-Verlag, Berlin etc., 1979, 243 pp. | MR | Zbl
[18] Schep A. R., “Daugavet type inequality for operators on $L^p$-spaces”, Positivity, 7:1–2 (2003), 103–111 | DOI | MR | Zbl
[19] Kusraev A. G., “Kantorovich's Principle in Action: $AW^\ast$-modules and injective Banach lattices”, Vladikavkaz Math. J., 14:1 (2012), 67–74 | MR | Zbl
[20] Gutman A. E., Lisovskaya S. A., “The boundedness principle for lattice-normed”, Siberian Math. J., 50:5 (2009), 830–837 | DOI | MR
[21] Shvidkoy R. V., “The largest linear space of operators satisfying the Daugavet equation in $L_1$”, Proc. Amer. Math., 120:3 (2002), 773–777 | DOI | MR
[22] Wickstead A. W., “$AL$-spaces and $AM$-spaces of operators”, Positivity, 4:3 (2000), 303–311 | DOI | MR | Zbl
[23] Kusraev A. G., Boolean Valued Analysis Approach to Injective Banach Lattices, Preprint No 1, Southern Math. Inst. VSC RAS, Vladikavkaz, 2011, 28 pp.
[24] Schaefer H. H., Banach Lattices and Positive Operators, Springer-Verlag, Berlin etc., 1974, 376 pp. | MR | Zbl
[25] Diestel J., Jarchow H., Tonge A., Absolutely Summing Operators, Cambridge Univ. Press, Cambridge etc., 1995, xv+474 pp. | MR | Zbl
[26] Levin V. L., “Tensor products and functors in categories of Banach spaces determined by $KB$-lineals”, Dokl. Acad. Nauk SSSR, 163:5 (1965), 1058–1060 | MR | Zbl